Iterative reconstruction of CT images without a regularization term

ABSTRACT

A method is disclosed for reconstructing image data of an examination object from measured data, wherein the measured data was captured previously during a relative rotary motion between a radiation source of a computed tomography system and the examination object. In at least one embodiment, the measured data is modified to achieve a particular grayscale characteristic of the image data to be reconstructed. The image data is calculated by way of an iterative algorithm using the modified measured data, wherein no arithmetic step for reducing noise is employed in the iterations.

PRIORITY STATEMENT

The present application hereby claims priority under 35 U.S.C. §119 onGerman patent application number DE 10 2010 022 305.0 filed Jun. 1,2010, the entire contents of which are hereby incorporated herein byreference.

FIELD

At least one embodiment of the invention generally relates to a methodfor reconstructing image data of an examination object from measureddata, this measured data having been captured previously during arelative rotary motion between a radiation source of a computedtomography system and the examination object.

BACKGROUND

Tomographic imaging methods are characterized in that inner structuresof an examination object can be examined without the need to perform anoperation on the examination object. One possible type of tomographicimage generation consists in recording a number of projections of theobject to be examined from different angles. A two-dimensional sectionalimage or a three-dimensional volume image of the examination object canbe calculated from these projections.

An example of such a tomographic imaging method is computed tomography.Methods for scanning an examination object with a CT system aregenerally known, with use being made here for example of circular scans,sequential circular scans with feed motion or spiral scans. Other typesof scans that are not based on circular motions are also possible, e.g.scans with linear segments. Using at least one x-ray source and at leastone opposing detector, absorption data of the examination object isrecorded from different recording angles and the absorption data orprojections collected in this way are allocated by way of correspondingreconstruction methods to sectional images through the examinationobject.

For reconstructing computed tomography images from x-ray CT datasets ofa computed tomography device (CT device), i.e. from the capturedprojections, what is known as Filtered Backprojection (FBP) is nowadaysused as the standard method. Following data capture a so-called“rebinning” step is normally performed, in which the data generated withthe fan-shaped beam emanating from the source is reordered so that it ispresent in a form as if the detector was being hit by x-ray beamstraveling toward it in parallel. The data is then transformed into thefrequency domain. Filtering takes place in the frequency domain, and thefiltered data is then transformed back. With the aid of the dataresorted and filtered in this way, a backprojection onto the individualvoxels within the volume of interest then takes place. However, with thetraditional FBP methods problems arise with so-called low-frequency conebeam artifacts and spiral artifacts as a result of the approximative wayin which they work. Furthermore, in traditional FBP methods the imagedefinition is linked to the image noise. The higher the definitionachieved, the higher also the image noise and vice versa.

Hence iterative reconstruction methods have recently been developed,with which at least some of these limitations can be eliminated. In suchan iterative reconstruction method initial image data is first of allreconstructed from the projection measured data. To this end, forexample, a convolution backprojection method can be used. Then from thisinitial image data synthetic projection data is generated with a“projector”, a projection operator, which should map the measuringsystem mathematically as closely as possible. The difference from themeasured signals is then backprojected with the operator adjoining theprojector and in this way a residual image is reconstructed, with whichthe initial image is updated. The updated image data can in turn be usedin a next iteration step to generate new synthetic projection data withthe aid of the projection operator, and from this again to form thedifference from the measured signals and to calculate a new residualimage, with which again the image data for the current iteration stageis improved, etc. Using such a method, image data can be reconstructedwhich has a relatively good image definition and nevertheless a lowimage noise. Examples of iterative reconstruction methods are thealgebraic reconstruction technique (ART), the simultaneous algebraicreconstruction technique (SART), iterated filtered backprojection(IFBP), or even statistical iterative image reconstruction techniques.

SUMMARY

In at least one embodiment of the invention, a method for the iterativereconstruction of CT images is demonstrated. Furthermore, acorresponding control and arithmetic unit, a CT system, a computerprogram and a computer program product are also demonstrated.

Advantageous embodiments and developments constitute the subject matterof subclaims.

In at least one embodiment of the inventive method for reconstructingimage data of an examination object from measured data this measureddata was previously captured during a relative rotary motion between aradiation source of a computed tomography system and the examinationobject. The measured data is modified to obtain a particular grayscalecharacteristic of the image data to be reconstructed. The image data iscalculated by way of an iterative algorithm using the modified measureddata. No arithmetic step for reducing noise is used in the iterations.

The image data is calculated iteratively. Thus several, i.e. at leasttwo, iterations take place, image data for the current iteration beingcalculated from image data for the preceding iteration in eachiteration. For the zero-th iteration the image data is determined fromthe measured data or the modified measured data.

In the known iterative CT image reconstruction methods a so-calledregularization term is employed, which for every iteration usessmoothing to remove some of the noise from the currently calculatediteration image. This arithmetic step is dispensed with in the inventivemethod. In other words, the algorithm for calculating the iterationimage from the image data for the last iteration does not contain such acomponent.

The lack of noise reduction in the iterations can be at least partiallyredressed in that the measured data is modified and is then used tocalculate the iteration images. This modification is such that the imagedata present after the iterative reconstruction has a particulargrayscale characteristic. This grayscale characteristic corresponds to atexture or a frequency characteristic of the image data. Preferably theparticular grayscale characteristic can be selected; i.e. a well-definedgrayscale characteristic which the reconstructed image data possessescan be selected.

The image data to be calculated by the iterative algorithm can betwo-dimensional sectional images or also three-dimensional volume imagesof the examination object.

In a development of at least one embodiment of the invention, a CTconvolution kernel specifying the particular grayscale characteristic isemployed during the modification of the measured data. As a result itcan be guaranteed that image data with a well-defined texture is presentat the output of the iteration loop. Such CT convolution kernels aree.g. known from conventional FBP image reconstruction. Examples are:body kernel B30, skull kernel H40. In particular the CT convolutionkernel can be employed in the form of its modulation transfer function.

it is particularly advantageous if after the iterative algorithm thecalculated image data undergoes noise-reduction processing. This mayinvolve filtering the image data. The noise reduction in this case takesplace, in contrast to conventional iterative calculation methods, not ineach iteration, but on conclusion of the iterations.

In an embodiment of the invention the particular grayscalecharacteristic is adjusted to the noise-reduction processing. The reasonfor this is that many noise-reduction processing operations require aparticular noise characteristic of the image data which is to beprocessed to be present; if it is not, the noise-reduction processingdoes not produce any satisfactory results. Thus to make the image datafor the iterative reconstruction compatible with such a requirement ofnoise-reduction processing, the iterative reconstruction takes placesuch that the particular grayscale characteristic is present as anoutput image. This is effected by the attributes of the modified imagedata.

According to an embodiment of the invention the noise-reductionprocessing includes non-linear filtering which smoothes the image datawhile preserving the edges. Such a smoothing does not take placeuniformly across the entire image; instead, smoothing preferably takesplace in homogeneous image regions, whereas in image regions with edgessmoothing is largely dispensed with. In this way the smoothing preservesthe edges.

It is possible to output the image obtained by the noise-reductionprocessing as a result image. Alternatively, after the noise-reductionprocessing the image data processed in this way can be merged with theunprocessed image data. In this way even better image attributes can beobtained where appropriate.

According to an embodiment of the invention, in the case of theiterative algorithm, first image data is calculated from the originalmeasured data, and image data for the following iterations is calculatedusing the modified measured data. This means that the unmodified imagedata is employed only to calculate the zero-th iteration image, whereasduring the following iterations only the modified measured data is stillemployed for image calculation.

It is advantageous if in the case of the iterative algorithm measureddata is calculated in each iteration from calculated image data and iscompared to the modified measured data. The use of the modified measureddata thus serves for comparison with synthetic, i.e. calculated,measured data. This can be effected by a simple or weighted differencecalculation. The aim of the iterative algorithm is to reconstruct theimage data such that measured data calculated from it matches themodified measured data as closely as possible. Correction data can thenbe calculated from the comparison and be used to correct the image data.

At least one embodiment of the inventive control and arithmetic unit isused for reconstructing image data for an examination object frommeasured data of a CT system. It includes a program memory for storingprogram code, whereby program code is present in it—where appropriatealong with other program code—which is suitable for executing a methodof the type described above or for effecting or controlling thisexecution. At least one embodiment of the inventive CT system includessuch a control and arithmetic unit. Furthermore, it may contain othercomponents which are required e.g. for capturing measured data.

At least one embodiment of the inventive computer program has programcode which is suitable for performing the method of the type describedabove if the computer program is run on a computer.

At least one embodiment of the inventive computer program productincludes program code stored on a computer-readable data carrier whichis suitable for performing the method of the type described above if thecomputer program is run on a computer.

BRIEF DESCRIPTION OF THE DRAWINGS

In the following, the invention is explained in greater detail on thebasis of an example embodiment. The drawings show:

FIG. 1: a first diagrammatic illustration of an example embodiment of acomputed tomography system with an image reconstruction component,

FIG. 2: a second diagrammatic illustration of an example embodiment of acomputed tomography system with an image reconstruction component,

FIG. 3: a flow chart.

DETAILED DESCRIPTION OF THE EXAMPLE EMBODIMENTS

Various example embodiments will now be described more fully withreference to the accompanying drawings in which only some exampleembodiments are shown. Specific structural and functional detailsdisclosed herein are merely representative for purposes of describingexample embodiments. The present invention, however, may be embodied inmany alternate forms and should not be construed as limited to only theexample embodiments set forth herein.

Accordingly, while example embodiments of the invention are capable ofvarious modifications and alternative forms, embodiments thereof areshown by way of example in the drawings and will herein be described indetail. It should be understood, however, that there is no intent tolimit example embodiments of the present invention to the particularforms disclosed. On the contrary, example embodiments are to cover allmodifications, equivalents, and alternatives falling within the scope ofthe invention. Like numbers refer to like elements throughout thedescription of the figures.

It will be understood that, although the terms first, second, etc. maybe used herein to describe various elements, these elements should notbe limited by these terms. These terms are only used to distinguish oneelement from another. For example, a first element could be termed asecond element, and, similarly, a second element could be termed a firstelement, without departing from the scope of example embodiments of thepresent invention. As used herein, the term “and/or,” includes any andall combinations of one or more of the associated listed items.

It will be understood that when an element is referred to as being“connected,” or “coupled,” to another element, it can be directlyconnected or coupled to the other element or intervening elements may bepresent. In contrast, when an element is referred to as being “directlyconnected,” or “directly coupled,” to another element, there are nointervening elements present. Other words used to describe therelationship between elements should be interpreted in a like fashion(e.g., “between,” versus “directly between,” “adjacent,” versus“directly adjacent,” etc.).

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of exampleembodiments of the invention. As used herein, the singular forms “a,”“an,” and “the,” are intended to include the plural forms as well,unless the context clearly indicates otherwise. As used herein, theterms “and/or” and “at least one of” include any and all combinations ofone or more of the associated listed items. It will be furtherunderstood that the terms “comprises,” “comprising,” “includes,” and/or“including,” when used herein, specify the presence of stated features,integers, steps, operations, elements, and/or components, but do notpreclude the presence or addition of one or more other features,integers, steps, operations, elements, components, and/or groupsthereof.

It should also be noted that in some alternative implementations, thefunctions/acts noted may occur out of the order noted in the figures.For example, two figures shown in succession may in fact be executedsubstantially concurrently or may sometimes be executed in the reverseorder, depending upon the functionality/acts involved.

Spatially relative terms, such as “beneath”, “below”, “lower”, “above”,“upper”, and the like, may be used herein for ease of description todescribe one element or feature's relationship to another element(s) orfeature(s) as illustrated in the figures. It will be understood that thespatially relative terms are intended to encompass differentorientations of the device in use or operation in addition to theorientation depicted in the figures. For example, if the device in thefigures is turned over, elements described as “below” or “beneath” otherelements or features would then be oriented “above” the other elementsor features. Thus, term such as “below” can encompass both anorientation of above and below. The device may be otherwise oriented(rotated 90 degrees or at other orientations) and the spatially relativedescriptors used herein are interpreted accordingly.

Although the terms first, second, etc. may be used herein to describevarious elements, components, regions, layers and/or sections, it shouldbe understood that these elements, components, regions, layers and/orsections should not be limited by these terms. These terms are used onlyto distinguish one element, component, region, layer, or section fromanother region, layer, or section. Thus, a first element, component,region, layer, or section discussed below could be termed a secondelement, component, region, layer, or section without departing from theteachings of the present invention.

FIG. 1 first of all illustrates diagrammatically a first computedtomography system C1 with an image reconstruction unit C21. This is aso-called third-generation CT device, to which however the invention isnot restricted. In the gantry housing C6 is a closed gantry (not shownhere) on which a first x-ray tube C2 with an opposing detector C3 isarranged. Optionally in the CT system shown here a second x-ray tube C4with an opposing detector C5 is arranged, so that thanks to theadditionally available emitter/detector combination a higher timeresolution can be achieved, or when using different x-ray energy spectrain the emitter/detector systems “dual-energy” examinations can also beperformed.

The CT system C1 furthermore has a patient couch C8, on which a patientcan be pushed into the measuring field during the examination along asystem axis C9, also called the Z axis, it being possible for thescanning itself to take place solely in the examination region ofinterest both as a pure circular scan without the patient being fedforward. The motion of the patient couch C8 relative to the gantry isaffected by a suitable motorization. During this motion the x-ray sourceC2 or C4 rotates around the patient in each case. In this case thedetector C3 or C5 runs in parallel opposite the x-ray source C2 or C4respectively, to capture projection measured data, which is then usedfor reconstructing sectional images.

Alternatively to a sequential scan, in which the patient is graduallypushed between the individual scans through the examination field, it isof course also possible to perform a spiral scan, in which the patientis continuously pushed along the system axis C9 through the examinationfield between x-ray tube C2 or C4 and detector C3 or C5 respectivelyduring the rotary scanning with the x-ray radiation. Thanks to themotion of the patient along the axis C9 and the simultaneous rotation ofthe x-ray source C2 or C4 a helical path is produced during a spiralscan for the x-ray source C2 or C4 relative to the patient during themeasurement. This path can also be achieved by pushing the gantry alongthe axis C9 while the patient remains stationary. Furthermore, it ispossible to move the patient continuously and periodically back andforth between two points.

The CT system 10 is controlled by a control and arithmetic unit C10 withcomputer program code Prg₁ to Prg_(n) present in a memory. It is pointedout that these computer program codes Prg₁ to Prg_(n) are of course alsocontained on an external storage medium and if required can be loadedinto the control and arithmetic unit C10.

From the control and arithmetic unit C10 acquisition control signals AScan be transmitted via a control interface 24 in order to control the CTsystem C1 according to particular measuring protocols. The acquisitioncontrol signals AS here relate to e.g. the x-ray tubes C2 and C4, itbeing possible for rules on their performance and the time points atwhich they are activated and deactivated to be made, as well as thegantry, it being possible for rules on its rotational speed to be made,as well as the table feed.

Since the control and arithmetic unit C10 has an input console,measurement parameters can be input by a user or operator of the CTdevice C1, and these then control the data capture in the form ofacquisition control signals AS. Information on currently usedmeasurement parameters can be displayed on the monitor of the controland arithmetic unit C10; in addition, further information relevant tothe operator can be displayed.

The projection measured data p or raw data acquired by the detector C3or C5 is passed via a raw data interface C23 to the control andarithmetic unit C10. This raw data p is then further processed in animage reconstruction component C21, if appropriate after suitablepreprocessing. The image reconstruction component C21 is implemented inthis exemplary embodiment in the control and arithmetic unit C10 in theform of software on a processor, e.g. in the form of one or more of thecomputer program codes Prg₁ to Prg_(n). In respect of the imagereconstruction it is the case, as already explained in respect of thecontrol of the measurement operation, that the computer program codesPrg₁ to Prg_(n) are also contained on an external storage medium and ifrequired can be loaded into the control and arithmetic unit C10.Furthermore, it is possible for the control of the measurement operationand the image reconstruction to be performed by different arithmeticunits.

The image data f reconstructed by the image reconstruction component C21is then stored in a memory C22 of the control and arithmetic unit C10and/or is output in the normal way on the monitor of the control andarithmetic unit C10. It can also be imported, via an interface not shownin FIG. 1, into a network connected to the computed tomography systemC1, for example a radiological information system (RIS), and stored in amass memory accessible there or output as images.

The control and arithmetic unit C10 can additionally also perform thefunction of an EKG, a line C12 being used to dissipate the EKGpotentials between patient and control and arithmetic unit C10. Inaddition the CT system C1 shown in FIG. 1 also has a contrast agentinjector C11, via which contrast agent can additionally be injected intothe patient's bloodstream, so that e.g. the patient's vessels, inparticular the ventricles of the beating heart, can be better displayed.This also makes it possible to perform perfusion measurements, for whichthe proposed method is likewise suitable.

FIG. 2 shows a C-arm system, in which in contrast to the CT system inFIG. 1 the housing C6 supports the C-arm C7, to which firstly the x-raytube C2 and secondly the opposing detector C3 are attached. The C-arm C7is swiveled for scanning likewise about a system axis C9, so thatscanning can take place from a plurality of scanning angles andcorresponding projection data p can be determined from a plurality ofprojection angles. The C-arm system C1 in FIG. 2, like the CT system inFIG. 1, has a control and arithmetic unit C10 of the type described forFIG. 1.

Embodiments of the invention can be used in both of the systems shown inFIGS. 1 and 2. Furthermore, it can in principle also be employed forother CT systems, e.g. for CT systems with a detector forming a completering.

In the following it is described how CT images can be obtained by way ofan iterative image reconstruction algorithm.

In conventional non-iterative image reconstruction methods so-calledcone beam artifacts occur in the CT image, as do spiral artifacts. Conebeam artifacts arise because the individual layers, i.e. the differentdetector lines, are assumed during image reconstruction to lie inparallel to one another, whereas in reality they are slanted in respectof one another. This effect increases as the number of detector linesincreases. Spiral artifacts in contrast stem from the data interpolationwhich in spiral scans is necessary in conventional reconstructionalgorithms in order to have data present for all Z positions androtation angles of the x-ray tube.

An advantage of iterative reconstruction methods compared toconventional non-iterative procedures, e.g. FBP (FilteredBackprojection), is that the cone beam artifacts and spiral artifactsdescribed do not occur in a CT image which was iterativelyreconstructed. Moreover, the image noise is also reduced compared toimages reconstructed in the conventional way. These two positive effectsare however achieved at different time points in the course of theiterative calculation: it is found that in iterative reconstruction theimage artifacts are already eliminated after a few, e.g. two, iterationcycles, whereas a convergence of the image noise is not achieved untilafter further iteration cycles.

In an iterative reconstruction the measured data p_(in) which typicallyis present in semi-parallel cone beam geometry, i.e. after azimuthalparallel rebinning, is used as an input signal. There then follows areconstruction of initial image data f₀ from the projection measureddata p_(in) by means of the backprojection operator Q^(T). To this end aconvolution backprojection method is used, for example. From thisinitial image data f₀ a projector Q (a projection operator which shouldemulate the measurement process mathematically as closely as possible)is used to generate synthetic projection data P_(syn). The differencebetween the synthetic projection data p_(syn), and the measured datap_(in) is then backprojected with the backprojection operator Q^(T)adjoining the projector Q and in this way a residual or correction imagef_(corr) is reconstructed, with which the initial image f₀ is updated.As a result the image f₁ of the first iteration is obtained. Thisupdated image data f₁ can in turn be used to generate new syntheticprojection data p_(syn) in a next iteration step with the aid of theprojection operator Q, again to calculate the difference from themeasured signals p_(in) from this and to calculate a new residual imagef_(corr), with which again the image data f₁ for the current iterationstage is improved and thus the image data f₂ for the next iterationstage is obtained, etc.

In addition to this basic mechanism, in iterative image reconstructionsa so-called regularization term is furthermore normally employed, whichreduces the image noise and determines its behavior. In each iterationcycle the regularization term is also used in addition to the correctionimage f_(corr), and effects a noise averaging and stabilization of thesolution and thus a convergence of the iterative algorithm.

In an iterative reconstruction based on a filtered backprojection (FBP)the update equation for the three-dimensional image volume f is:f _(k+1) =f _(k) +[α·Q ^(T) ·K·(Q·f _(k) −p _(in))−γ·R(f _(k))]  Formula(1)Here, f_(k+1) is the image of the k+1-th iteration which is calculatedfrom the image f_(k) of the k-th iteration.The correction term—this corresponds to the correction image f_(corr)—isα·Q^(T)·K·(Q·f_(k)−p_(in)). Here, α is a constant factor whichdetermines the degree of the correction of the image f_(k) by thecorrection image f_(corr). A Ramlak kernel (linear ramp in the frequencyspace) is normally selected as kernel K. The correction term correctsimage errors that are caused by the non-exact backprojector Q^(T).

The correction term corresponds to a highpass filtering of the imagef_(k). For this reason the correction term effects an increase in theimage noise. The regularization term counteracts this. Without the useof the regularization term the image noise would hence increase fromiteration to iteration. The regularization term is γ·R(f_(k)), where γrepresents a constant factor which determines the degree of theadmixture of the regularization term. R(f_(k)) is a non-linear highpassfilter which is applied to the image f_(k) of the k-th iteration stage.In the update equation the regularization term works like a non-linearlowpass because of the minus sign.

If formula (1) is examined, the correction term represents a componentwhich contains a switch from the image data space to the measured dataspace. Because of the necessary forward and backward projectioncalculations this is compute-intensive and thus costly in terms ofresources and time. In contrast, the regularization term represents acomponent which corresponds to a pure manipulation in the image dataspace, which requires less computing effort.

The function of the correction term is to eliminate image errors,whereas the regularization term effects a denoising of the image. Asalready mentioned, the aim of eliminating the image errors is generallyachieved with significantly fewer iterations than the denoising of theimage. However, each further iteration requires considerable computingeffort, so that it would be advantageous to exit the iteration loopafter eliminating the image errors.

Hence as shown in FIG. 3 the iterative algorithm is applied withoutusing the regularization term. It is thus employed as an update equationf _(k+1) =f _(k) +α·Q ^(T) ·K·(Q·f _(k) −P′ _(in))  Formula (2).

As explained above, the initial image f₀ is calculated from the measureddata p_(in). To calculate each correction image f_(corr) use is made notof the measured data p_(in) but of modified measured data P′_(in)obtained therefrom, the function of which is explained in more detailbelow. At the point at which the curly bracket is drawn in, theregularization term according to formula (1) would normally be employed,but this is dispensed with according to formula (2).

Since the noise reduction is not brought about by the regularizationterm, a non-linear image filter IF is employed for noise reduction afterthe end of the iteration, i.e. if the number of iterations n has reacheda particular maximum number N_(max). Normally such image filters worksatisfactorily only if the image processed by them has a particulargrayscale characteristic or texture. It must therefore be ensured thatthe image which the iterative algorithm supplies according to formula(2) and FIG. 3 has a defined status in respect of the image noise. Asalready explained, the correction term increases the image noise fromiteration to iteration because of its highpass effect, so that if theregularization term is simply omitted, no defined image noise of theresult image can be effected by the iterative algorithm.

Hence the iterative algorithm according to formula (2) should benoise-neutral; this means that the noise increase is prevented by thecorrection term. This occurs because the measured values p_(in) arefiltered two-dimensionally according to formula (3). The measured valuesp_(in) are present here in two-dimensional form for each projectionangle, in accordance with the two-dimensional detector, which extends inthe channel and line direction.P′ _(in)=((Q·Q ^(T))_(xy) ·I/K){circle around (x)}(Q·Q ^(T))_(z) ·p_(in)  Formula (3)

(Q·Q^(T))_(xy) designates the transverse component, i.e. the proportionworking in the channel direction or within the plane of a layer of theexamination object, and (Q·Q^(T))_(z) the axial component, i.e. theproportion of the three-dimensional operator (Q·Q^(T)) working in theline direction Z or perpendicular to the layer plane. This operator(Q·Q^(T)) essentially characterizes the interpolation functions in theforward projection and backprojection. The backprojection is typicallyvoxel-driven, i.e. the detector signal assigned to a voxel must bedetermined by (e.g. linear) interpolation. Similarly during theprojection of the image signal to calculate the line integral the imagesignals must be interpolated voxel by voxel (linearly). (Q·Q^(T))_(xy)and (Q·Q^(T))_(z) work as lowpass; they are both short-range filters.

The operator I is a CT convolution kernel that can be stipulated by theuser, i.e. by the person evaluating the CT image, normally aradiologist. In the case of a filtered backprojection such a CT filterkernel is applied in the filter step; this determines the noisecharacteristic of the result ing image. In the case of the presentiterative algorithm too, the CT filter kernel I determines the noisecharacteristic of the image output by the iterative algorithm. Theexpression I/K corresponds to the modulation transfer function of the CTimage recording. In other words, in addition to the lowpass filteringexplained above, the input signal is lowpass-filtered with themodulation transfer function of the input kernel I.

P′_(in) is thus a lowpass-filtered version of the measured data p_(in),with a particular frequency characteristic stipulated by the kernel I.

In the correction term the synthetic data p_(syn) is not compared to themeasured data p_(in) according to formula (2), but to the modifiedmeasured data P′_(in). Because of the nature of the modified measureddata P′_(in) this firstly means that no noise increase in the iterationimage is added by the correction image f_(corr), and secondly that afterthe last iteration the result image has the frequency characteristic orgrayscale characteristic stipulated by the operator I. Thus through theuse of the modified data P′_(in) a dedicated and desired noisecharacteristic of the image present after the iteration is aborted isenforced.

By using a suitable filter IF after the end of the iterativereconstruction a desired definition-to-noise ratio of the image can beset. Non-linear three-dimensional image filters are suitable for this.It is advantageous to use a filter which firstly performs a smoothing ofthe image in homogeneous regions; this enables the noise power spectrumto be set and thus direct control of the desired noise texture. Secondlythe filter can exempt non-homogeneous regions in which a significantstructure is present in the image from smoothing, so that edges arerecessed during smoothing. By using a suitable filter function it iseven possible to reinforce the edges. Overall such a filter thus effectssmoothing while preserving the edges. Such a filter can be appliedeither simply or iteratively to the image to be filtered.

A specific example of such a filter can be found in our own subsequentlypublished application DE 10 2009 039 987.9, the entire contents of whichare hereby incorporated herein by reference. A filter function isreproduced in formula (8) of this application. This can also be appliedin simplified terms, in particular in that only the term designated byII, and not the term designated by I, is employed. Another specificexample of such a filter, which in terms of contents corresponds asclosely as possible to the first example, was given in a lecture atRSNA2009 in Chicago in the Physics session (CT: New Methods) on Nov. 29,2009 from 11:15-11:25 by Dr. T. Flohr, the entire contents of which arehereby incorporated herein by reference.

The image f_(IR-IF) present after processing by the filter IF can beoutput as a result image f_(Final).

Alternatively it is possible to merge the filtered image f_(IR-IF) withthe image f_(k) _(max) present after the iteration and before thefiltering according to:f _(Final) =β·f _(k) _(max) +(1−β)·f _(IR-IF)  Formula (4)

Here β is a parameter between 0 and 1. As a result, an optimization ofthe grayscale characteristic of the result image f_(Final) can beachieved.

It has thus been shown that during an iterative reconstruction theregularization term can be done away with, as a result of which feweriterations are necessary until convergence is reached. Instead of theregularization term which normally determines the noise characteristicof the result image, a suitable image filter is applied downstream ofthe iterative algorithm. This corresponds to a decoupling of correctionterm and regularization term during the iterative image reconstruction.In order to make a dedicated noise characteristic available for theinput image of the image filter, the measured data undergoes atwo-dimensional filtering using a filter kernel which stipulates thisnoise characteristic.

The invention was described above using an example embodiment. It shouldbe understood that numerous changes and modifications are possible,without going beyond the framework of the invention.

The patent claims filed with the application are formulation proposalswithout prejudice for obtaining more extensive patent protection. Theapplicant reserves the right to claim even further combinations offeatures previously disclosed only in the description and/or drawings.

The example embodiment or each example embodiment should not beunderstood as a restriction of the invention. Rather, numerousvariations and modifications are possible in the context of the presentdisclosure, in particular those variants and combinations which can beinferred by the person skilled in the art with regard to achieving theobject for example by combination or modification of individual featuresor elements or method steps that are described in connection with thegeneral or specific part of the description and are contained in theclaims and/or the drawings, and, by way of combinable features, lead toa new subject matter or to new method steps or sequences of methodsteps, including insofar as they concern production, testing andoperating methods.

References back that are used in dependent claims indicate the furtherembodiment of the subject matter of the main claim by way of thefeatures of the respective dependent claim; they should not beunderstood as dispensing with obtaining independent protection of thesubject matter for the combinations of features in the referred-backdependent claims. Furthermore, with regard to interpreting the claims,where a feature is concretized in more specific detail in a subordinateclaim, it should be assumed that such a restriction is not present inthe respective preceding claims.

Since the subject matter of the dependent claims in relation to theprior art on the priority date may form separate and independentinventions, the applicant reserves the right to make them the subjectmatter of independent claims or divisional declarations. They mayfurthermore also contain independent inventions which have aconfiguration that is independent of the subject matters of thepreceding dependent claims.

Further, elements and/or features of different example embodiments maybe combined with each other and/or substituted for each other within thescope of this disclosure and appended claims.

Still further, any one of the above-described and other example featuresof the present invention may be embodied in the form of an apparatus,method, system, computer program, tangible computer readable medium andtangible computer program product. For example, of the aforementionedmethods may be embodied in the form of a system or device, including,but not limited to, any of the structure for performing the methodologyillustrated in the drawings.

Even further, any of the aforementioned methods may be embodied in theform of a program. The program may be stored on a tangible computerreadable medium and is adapted to perform any one of the aforementionedmethods when run on a computer device (a device including a processor).Thus, the tangible storage medium or tangible computer readable medium,is adapted to store information and is adapted to interact with a dataprocessing facility or computer device to execute the program of any ofthe above mentioned embodiments and/or to perform the method of any ofthe above mentioned embodiments.

The tangible computer readable medium or tangible storage medium may bea built-in medium installed inside a computer device main body or aremovable tangible medium arranged so that it can be separated from thecomputer device main body. Examples of the built-in tangible mediuminclude, but are not limited to, rewriteable non-volatile memories, suchas ROMs and flash memories, and hard disks. Examples of the removabletangible medium include, but are not limited to, optical storage mediasuch as CD-ROMs and DVDs; magneto-optical storage media, such as MOs;magnetism storage media, including but not limited to floppy disks(trademark), cassette tapes, and removable hard disks; media with abuilt-in rewriteable non-volatile memory, including but not limited tomemory cards; and media with a built-in ROM, including but not limitedto ROM cassettes; etc. Furthermore, various information regarding storedimages, for example, property information, may be stored in any otherform, or it may be provided in other ways.

Example embodiments being thus described, it will be obvious that thesame may be varied in many ways. Such variations are not to be regardedas a departure from the spirit and scope of the present invention, andall such modifications as would be obvious to one skilled in the art areintended to be included within the scope of the following claims.

What is claimed is:
 1. A method for reconstructing image data of anexamination object from measured data, wherein the measured data iscaptured during a relative rotary motion between a radiation source of acomputed tomography (CT) system and the examination object, the methodcomprising: modifying the measured data to achieve a particulargrayscale characteristic of the image data to be reconstructed; andcalculating the image data by way of an iterative algorithm using themodified measured data, the iterative algorithm including a correctionterm for iteratively correcting image errors, wherein upon a terminationof the iterative algorithm, the calculated image data undergoes anoise-reduction processing.
 2. The method as claimed in claim 1, whereinthe modifying the measured data is based on a CT convolution kernel,which stipulates the particular grayscale characteristic.
 3. The methodas claimed in claim 2, wherein the particular grayscale characteristicis adapted to the noise-reduction processing.
 4. The method as claimedin claim 2, wherein the noise-reduction processing includes a non-linearfiltering which smoothes the image data while preserving edges of theimage data.
 5. The method as claimed in claim 1, wherein the particulargrayscale characteristic is adapted to the noise-reduction processing.6. The method as claimed in claim 1, wherein the noise-reductionprocessing includes a non-linear filtering which smoothes the image datawhile preserving edges of the image data.
 7. The method as claimed inclaim 1, wherein, after the noise-reduction processing, the image dataprocessed is merged with the unprocessed image data.
 8. The method asclaimed in claim 1, wherein the calculating the image data comprises:calculating first image data from the measured data, and calculatingsubsequent image data during subsequent iterations of the iterativealgorithm using the modified measured data.
 9. The method as claimed inclaim 1, further comprising: calculating measured data during eachiteration of the iterative algorithm from the calculated image data; andcomparing the calculated measured data with the modified measured data.10. The method as claimed in claim 9, wherein further comprising:calculating correction data is based on the comparing; and correctingthe calculated image data based on the calculated correction data.
 11. Anon-transitory computer program comprising: program code configured toperform the method as claimed in claim 1 when the computer program isrun on a computer.
 12. A non-transitory computer readable mediumincluding a computer program product, the computer program productcomprising computer instructions, which when executed by a processor,causes the processor to perform the method of claim
 1. 13. The method asclaimed in claim 1, wherein the iterative algorithm further includes aregularization term which is not used during the iteratively correctingimage errors.
 14. The method as claimed in claim 13, wherein theiterative algorithm is based on a decoupling of the correction term andthe regularization term.
 15. The method as claimed in claim 14, whereinthe decoupling results in a faster convergence of the iterativealgorithm compared to a reconstruction method based on an iterativealgorithm with a coupled correction and regularization terms.
 16. Acontrol and arithmetic unit for reconstructing image data of anexamination object from measured data of a computer tomography (CT)system, the control and arithmetic unit comprising: a program memoryconfigured to store program code, the program code, when executed,performing functions including: modifying the measured data to achieve aparticular grayscale characteristic of the image data to bereconstructed; and calculating the image data by way of an iterativealgorithm using the modified measured data, the iterative algorithmincluding a correction term for iteratively correcting image errors,wherein upon a termination of the iterative algorithm, the calculatedimage data undergoes a noise-reduction processing.
 17. A CT systemcomprising: a control and arithmetic unit as claimed in claim 16.